import datetime

import seaborn as sns

import time

​

import matplotlib.pyplot as plt

%matplotlib inline

from sklearn.decomposition import PCA

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import math

​

​

from sklearn.metrics import mean_squared_error

from sklearn.preprocessing import StandardScaler

from sklearn.model_selection import cross_val_score

from sklearn.preprocessing import LabelEncoder 

from sklearn.preprocessing import MinMaxScaler

from sklearn.preprocessing import minmax_scale

from sklearn.preprocessing import MaxAbsScaler

from sklearn.preprocessing import StandardScaler

from sklearn.preprocessing import RobustScaler

from sklearn.preprocessing import Normalizer

from sklearn.metrics import r2_score

from sklearn.metrics import accuracy_score

​

​

​

# Other packages

import numpy as np

import pandas as pd

import re

import scipy as sp

import xgboost as xgb

import matplotlib.pyplot as plt

from numpy import concatenate

from pandas import DataFrame, Series, read_csv, scatter_matrix

​

import warnings

warnings.filterwarnings("ignore")

​

​

SP500_TechIndicator = read_csv('SP500_tech_Indicator.csv')

#SP500_TechIndicator = SP500_TechIndicator.drop(['Unnamed: 0'], axis=1)

SP500_TechIndicator.shape

SP500_TechIndicator

#Activision_Blizzard_FFT

Activision_Blizzard_FT = SP500_TechIndicator[['Date', 'Activision_Blizzard_Close']]

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​

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Activision_Blizzard_Close_fft = np.fft.fft(np.asarray(Activision_Blizzard_FT['Activision_Blizzard_Close'].tolist()))

Activision_Blizzard_fft_df = pd.DataFrame({'Activision_Blizzard_final_fft':Activision_Blizzard_Close_fft})

Activision_Blizzard_fft_df['Activision_Blizzard_fft_absolute'] = Activision_Blizzard_fft_df['Activision_Blizzard_final_fft'].apply(lambda x: np.abs(x))

Activision_Blizzard_fft_df['Activision_Blizzard_fft_angle'] = Activision_Blizzard_fft_df['Activision_Blizzard_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Activision_Blizzard_fft_list = np.asarray(Activision_Blizzard_fft_df['Activision_Blizzard_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Activision_Blizzard_fft_list_m10= np.copy(Activision_Blizzard_fft_list); Activision_Blizzard_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Activision_Blizzard_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Activision_Blizzard_FT['Activision_Blizzard_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Activision Blizzard(close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

Activision_Blizzard_fft_df

#Alphabet_Inc_Class_A_FFT

Alphabet_Inc_Class_A_FT = SP500_TechIndicator[['Date', 'Alphabet_Inc_Class_A_Close']]

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​

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Alphabet_Inc_Class_A_Close_fft = np.fft.fft(np.asarray(Alphabet_Inc_Class_A_FT['Alphabet_Inc_Class_A_Close'].tolist()))

Alphabet_Inc_Class_A_fft_df = pd.DataFrame({'Alphabet_Inc_Class_A_final_fft':Alphabet_Inc_Class_A_Close_fft})

Alphabet_Inc_Class_A_fft_df['Alphabet_Inc_Class_A_fft_absolute'] = Alphabet_Inc_Class_A_fft_df['Alphabet_Inc_Class_A_final_fft'].apply(lambda x: np.abs(x))

Alphabet_Inc_Class_A_fft_df['Alphabet_Inc_Class_A_fft_angle'] = Alphabet_Inc_Class_A_fft_df['Alphabet_Inc_Class_A_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Alphabet_Inc_Class_A_fft_list = np.asarray(Alphabet_Inc_Class_A_fft_df['Alphabet_Inc_Class_A_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Alphabet_Inc_Class_A_fft_list_m10= np.copy(Alphabet_Inc_Class_A_fft_list); Alphabet_Inc_Class_A_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Alphabet_Inc_Class_A_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Alphabet_Inc_Class_A_FT['Alphabet_Inc_Class_A_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Alphabet_Inc_Class_A(close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#ATT_FFT

ATT_FT = SP500_TechIndicator[['Date', 'ATT_Close']]

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​

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ATT_Close_fft = np.fft.fft(np.asarray(ATT_FT['ATT_Close'].tolist()))

ATT_fft_df = pd.DataFrame({'ATT_final_fft':ATT_Close_fft})

ATT_fft_df['ATT_fft_absolute'] = ATT_fft_df['ATT_final_fft'].apply(lambda x: np.abs(x))

ATT_fft_df['ATT_fft_angle'] = ATT_fft_df['ATT_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

ATT_fft_list = np.asarray(ATT_fft_df['ATT_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    ATT_fft_list_m10= np.copy(ATT_fft_list); ATT_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(ATT_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(ATT_FT['ATT_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: ATT (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#CBS_FFT

CBS_FT = SP500_TechIndicator[['Date', 'CBS_Close']]

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​

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CBS_Close_fft = np.fft.fft(np.asarray(CBS_FT['CBS_Close'].tolist()))

CBS_fft_df = pd.DataFrame({'CBS_final_fft':CBS_Close_fft})

CBS_fft_df['CBS_fft_absolute'] = CBS_fft_df['CBS_final_fft'].apply(lambda x: np.abs(x))

CBS_fft_df['CBS_fft_angle'] = CBS_fft_df['CBS_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

CBS_fft_list = np.asarray(CBS_fft_df['CBS_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    CBS_fft_list_m10= np.copy(CBS_fft_list); CBS_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(CBS_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(CBS_FT['CBS_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: CBS (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#CenturyLink_FFT

CenturyLink_FT = SP500_TechIndicator[['Date', 'CenturyLink_Close']]

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CenturyLink_Close_fft = np.fft.fft(np.asarray(CenturyLink_FT['CenturyLink_Close'].tolist()))

CenturyLink_fft_df = pd.DataFrame({'CenturyLink_final_fft':CenturyLink_Close_fft})

CenturyLink_fft_df['CenturyLink_fft_absolute'] = CenturyLink_fft_df['CenturyLink_final_fft'].apply(lambda x: np.abs(x))

CenturyLink_fft_df['CenturyLink_fft_angle'] = CenturyLink_fft_df['CenturyLink_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

CenturyLink_fft_list = np.asarray(CenturyLink_fft_df['CenturyLink_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    CenturyLink_fft_list_m10= np.copy(CenturyLink_fft_list); CenturyLink_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(CenturyLink_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(CenturyLink_FT['CenturyLink_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: CenturyLink (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Comcast_FFT

Comcast_FT = SP500_TechIndicator[['Date', 'Comcast_Close']]

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​

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Comcast_Close_fft = np.fft.fft(np.asarray(Comcast_FT['Comcast_Close'].tolist()))

Comcast_fft_df = pd.DataFrame({'Comcast_final_fft':Comcast_Close_fft})

Comcast_fft_df['Comcast_fft_absolute'] = Comcast_fft_df['Comcast_final_fft'].apply(lambda x: np.abs(x))

Comcast_fft_df['Comcast_fft_angle'] = Comcast_fft_df['Comcast_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Comcast_fft_list = np.asarray(Comcast_fft_df['Comcast_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Comcast_fft_list_m10= np.copy(Comcast_fft_list); Comcast_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Comcast_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Comcast_FT['Comcast_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Comcast (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Discovery_Class_A_FFT

Discovery_Class_A_FT = SP500_TechIndicator[['Date', 'Discovery_Class_A_Close']]

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​

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Discovery_Class_A_Close_fft = np.fft.fft(np.asarray(Discovery_Class_A_FT['Discovery_Class_A_Close'].tolist()))

Discovery_Class_A_fft_df = pd.DataFrame({'Discovery_Class_A_final_fft':Discovery_Class_A_Close_fft})

Discovery_Class_A_fft_df['Discovery_Class_A_fft_absolute'] = Discovery_Class_A_fft_df['Discovery_Class_A_final_fft'].apply(lambda x: np.abs(x))

Discovery_Class_A_fft_df['Discovery_Class_A_fft_angle'] = Discovery_Class_A_fft_df['Discovery_Class_A_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Discovery_Class_A_fft_list = np.asarray(Discovery_Class_A_fft_df['Discovery_Class_A_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Discovery_Class_A_fft_list_m10= np.copy(Discovery_Class_A_fft_list); Discovery_Class_A_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Discovery_Class_A_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Discovery_Class_A_FT['Discovery_Class_A_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Discovery_Class_A (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Discovery_Class_C_FFT

Discovery_Class_C_FT = SP500_TechIndicator[['Date', 'Discovery_Class_C_Close']]

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​

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Discovery_Class_C_Close_fft = np.fft.fft(np.asarray(Discovery_Class_C_FT['Discovery_Class_C_Close'].tolist()))

Discovery_Class_C_fft_df = pd.DataFrame({'Discovery_Class_C_final_fft':Discovery_Class_C_Close_fft})

Discovery_Class_C_fft_df['Discovery_Class_C_fft_absolute'] = Discovery_Class_C_fft_df['Discovery_Class_C_final_fft'].apply(lambda x: np.abs(x))

Discovery_Class_C_fft_df['Discovery_Class_C_fft_angle'] = Discovery_Class_C_fft_df['Discovery_Class_C_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Discovery_Class_C_fft_list = np.asarray(Discovery_Class_C_fft_df['Discovery_Class_C_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Discovery_Class_C_fft_list_m10= np.copy(Discovery_Class_C_fft_list); Discovery_Class_C_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Discovery_Class_C_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Discovery_Class_C_FT['Discovery_Class_C_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Discovery_Class_C (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Dish_FFT

Dish_FT = SP500_TechIndicator[['Date', 'Dish_Close']]

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​

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Dish_Close_fft = np.fft.fft(np.asarray(Dish_FT['Dish_Close'].tolist()))

Dish_fft_df = pd.DataFrame({'Dish_final_fft':Dish_Close_fft})

Dish_fft_df['Dish_fft_absolute'] = Dish_fft_df['Dish_final_fft'].apply(lambda x: np.abs(x))

Dish_fft_df['Dish_fft_angle'] = Dish_fft_df['Dish_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Dish_fft_list = np.asarray(Dish_fft_df['Dish_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Dish_fft_list_m10= np.copy(Dish_fft_list); Dish_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Dish_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Dish_FT['Dish_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Dish (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Electronic_Arts_FFT

Electronic_Arts_FT = SP500_TechIndicator[['Date', 'Electronic_Arts_Close']]

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​

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Electronic_Arts_Close_fft = np.fft.fft(np.asarray(Electronic_Arts_FT['Electronic_Arts_Close'].tolist()))

Electronic_Arts_fft_df = pd.DataFrame({'Electronic_Arts_final_fft':Electronic_Arts_Close_fft})

Electronic_Arts_fft_df['Electronic_Arts_fft_absolute'] = Electronic_Arts_fft_df['Electronic_Arts_final_fft'].apply(lambda x: np.abs(x))

Electronic_Arts_fft_df['Electronic_Arts_fft_angle'] = Electronic_Arts_fft_df['Electronic_Arts_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Electronic_Arts_fft_list = np.asarray(Electronic_Arts_fft_df['Electronic_Arts_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Electronic_Arts_fft_list_m10= np.copy(Electronic_Arts_fft_list); Electronic_Arts_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Electronic_Arts_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Electronic_Arts_FT['Electronic_Arts_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Electronic_Arts (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Facebook_FFT

Facebook_FT = SP500_TechIndicator[['Date', 'Facebook_Close']]

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​

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Facebook_Close_fft = np.fft.fft(np.asarray(Facebook_FT['Facebook_Close'].tolist()))

Facebook_fft_df = pd.DataFrame({'Facebook_final_fft':Facebook_Close_fft})

Facebook_fft_df['Facebook_fft_absolute'] = Facebook_fft_df['Facebook_final_fft'].apply(lambda x: np.abs(x))

Facebook_fft_df['Facebook_fft_angle'] = Facebook_fft_df['Facebook_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Facebook_fft_list = np.asarray(Facebook_fft_df['Facebook_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Facebook_fft_list_m10= np.copy(Facebook_fft_list); Facebook_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Facebook_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Facebook_FT['Facebook_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Facebook (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Interpublic_Group_FFT

Interpublic_Group_FT = SP500_TechIndicator[['Date', 'Interpublic_Group_Close']]

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​

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Interpublic_Group_Close_fft = np.fft.fft(np.asarray(Interpublic_Group_FT['Interpublic_Group_Close'].tolist()))

Interpublic_Group_fft_df = pd.DataFrame({'Interpublic_Group_final_fft':Interpublic_Group_Close_fft})

Interpublic_Group_fft_df['Interpublic_Group_fft_absolute'] = Interpublic_Group_fft_df['Interpublic_Group_final_fft'].apply(lambda x: np.abs(x))

Interpublic_Group_fft_df['Interpublic_Group_fft_angle'] = Interpublic_Group_fft_df['Interpublic_Group_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Interpublic_Group_fft_list = np.asarray(Interpublic_Group_fft_df['Interpublic_Group_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Interpublic_Group_fft_list_m10= np.copy(Interpublic_Group_fft_list); Interpublic_Group_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Interpublic_Group_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Interpublic_Group_FT['Interpublic_Group_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Interpublic_Group (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Netflix_FFT

Netflix_FT = SP500_TechIndicator[['Date', 'Netflix_Close']]

​

​

​

Netflix_Close_fft = np.fft.fft(np.asarray(Netflix_FT['Netflix_Close'].tolist()))

Netflix_fft_df = pd.DataFrame({'Netflix_final_fft':Netflix_Close_fft})

Netflix_fft_df['Netflix_fft_absolute'] = Netflix_fft_df['Netflix_final_fft'].apply(lambda x: np.abs(x))

Netflix_fft_df['Netflix_fft_angle'] = Netflix_fft_df['Netflix_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Netflix_fft_list = np.asarray(Netflix_fft_df['Netflix_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Netflix_fft_list_m10= np.copy(Netflix_fft_list); Netflix_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Netflix_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Netflix_FT['Netflix_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Netflix (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#News_Corp_Class_A_FFT

News_Corp_Class_A_FT = SP500_TechIndicator[['Date', 'News_Corp_Class_A_Close']]

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​

​

News_Corp_Class_A_Close_fft = np.fft.fft(np.asarray(News_Corp_Class_A_FT['News_Corp_Class_A_Close'].tolist()))

News_Corp_Class_A_fft_df = pd.DataFrame({'News_Corp_Class_A_final_fft':News_Corp_Class_A_Close_fft})

News_Corp_Class_A_fft_df['News_Corp_Class_A_fft_absolute'] = News_Corp_Class_A_fft_df['News_Corp_Class_A_final_fft'].apply(lambda x: np.abs(x))

News_Corp_Class_A_fft_df['News_Corp_Class_A_fft_angle'] = News_Corp_Class_A_fft_df['News_Corp_Class_A_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

News_Corp_Class_A_fft_list = np.asarray(News_Corp_Class_A_fft_df['News_Corp_Class_A_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    News_Corp_Class_A_fft_list_m10= np.copy(News_Corp_Class_A_fft_list); News_Corp_Class_A_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(News_Corp_Class_A_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(News_Corp_Class_A_FT['News_Corp_Class_A_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: News_Corp_Class_A (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#News_Corp_Class_B_FFT

News_Corp_Class_B_FT = SP500_TechIndicator[['Date', 'News_Corp_Class_B_Close']]

​

​

​

News_Corp_Class_B_Close_fft = np.fft.fft(np.asarray(News_Corp_Class_B_FT['News_Corp_Class_B_Close'].tolist()))

News_Corp_Class_B_fft_df = pd.DataFrame({'News_Corp_Class_B_final_fft':News_Corp_Class_B_Close_fft})

News_Corp_Class_B_fft_df['News_Corp_Class_B_fft_absolute'] = News_Corp_Class_B_fft_df['News_Corp_Class_B_final_fft'].apply(lambda x: np.abs(x))

News_Corp_Class_B_fft_df['News_Corp_Class_B_fft_angle'] = News_Corp_Class_B_fft_df['News_Corp_Class_B_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

News_Corp_Class_B_fft_list = np.asarray(News_Corp_Class_B_fft_df['News_Corp_Class_B_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    News_Corp_Class_B_fft_list_m10= np.copy(News_Corp_Class_B_fft_list); News_Corp_Class_B_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(News_Corp_Class_B_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(News_Corp_Class_B_FT['News_Corp_Class_B_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: News_Corp_Class_B (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Omnicom_Group_FFT

Omnicom_Group_FT = SP500_TechIndicator[['Date', 'Omnicom_Group_Close']]

​

​

​

Omnicom_Group_Close_fft = np.fft.fft(np.asarray(Omnicom_Group_FT['Omnicom_Group_Close'].tolist()))

Omnicom_Group_fft_df = pd.DataFrame({'Omnicom_Group_final_fft':Omnicom_Group_Close_fft})

Omnicom_Group_fft_df['Omnicom_Group_fft_absolute'] = Omnicom_Group_fft_df['Omnicom_Group_final_fft'].apply(lambda x: np.abs(x))

Omnicom_Group_fft_df['Omnicom_Group_fft_angle'] = Omnicom_Group_fft_df['Omnicom_Group_final_fft'].apply(lambda x: np.angle(x))

​

plt.figure(figsize=(14, 7), dpi=100)

Omnicom_Group_fft_list = np.asarray(Omnicom_Group_fft_df['Omnicom_Group_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Omnicom_Group_fft_list_m10= np.copy(Omnicom_Group_fft_list); Omnicom_Group_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Omnicom_Group_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Omnicom_Group_FT['Omnicom_Group_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Omnicom_Group (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#Take_Two_Interactive_FFT

Take_Two_Interactive_FT = SP500_TechIndicator[['Date', 'Take_Two_Interactive_Close']]

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Take_Two_Interactive_Close_fft = np.fft.fft(np.asarray(Take_Two_Interactive_FT['Take_Two_Interactive_Close'].tolist()))

Take_Two_Interactive_fft_df = pd.DataFrame({'Take_Two_Interactive_final_fft':Take_Two_Interactive_Close_fft})

Take_Two_Interactive_fft_df['Take_Two_Interactive_fft_absolute'] = Take_Two_Interactive_fft_df['Take_Two_Interactive_final_fft'].apply(lambda x: np.abs(x))

Take_Two_Interactive_fft_df['Take_Two_Interactive_fft_angle'] = Take_Two_Interactive_fft_df['Take_Two_Interactive_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

Take_Two_Interactive_fft_list = np.asarray(Take_Two_Interactive_fft_df['Take_Two_Interactive_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Take_Two_Interactive_fft_list_m10= np.copy(Take_Two_Interactive_fft_list); Take_Two_Interactive_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Take_Two_Interactive_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Take_Two_Interactive_FT['Take_Two_Interactive_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Take_Two_Interactive (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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#Twitter_FFT

Twitter_FT = SP500_TechIndicator[['Date', 'Twitter_Close']]

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Twitter_Close_fft = np.fft.fft(np.asarray(Twitter_FT['Twitter_Close'].tolist()))

Twitter_fft_df = pd.DataFrame({'Twitter_final_fft':Twitter_Close_fft})

Twitter_fft_df['Twitter_fft_absolute'] = Twitter_fft_df['Twitter_final_fft'].apply(lambda x: np.abs(x))

Twitter_fft_df['Twitter_fft_angle'] = Twitter_fft_df['Twitter_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

Twitter_fft_list = np.asarray(Twitter_fft_df['Twitter_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Twitter_fft_list_m10= np.copy(Twitter_fft_list); Twitter_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Twitter_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Twitter_FT['Twitter_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Twitter (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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plt.figure(figsize=(14, 7), dpi=100)

fft_list = np.asarray(fft_df['fft'].tolist())

for num_ in [3, 6, 9, 100]:

    fft_list_m10= np.copy(fft_list); fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(data_FT['Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: J P Morgan (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

#TripAdvisor_FFT

TripAdvisor_FT = SP500_TechIndicator[['Date', 'TripAdvisor_Close']]

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TripAdvisor_Close_fft = np.fft.fft(np.asarray(TripAdvisor_FT['TripAdvisor_Close'].tolist()))

TripAdvisor_fft_df = pd.DataFrame({'TripAdvisor_final_fft':TripAdvisor_Close_fft})

TripAdvisor_fft_df['TripAdvisor_fft_absolute'] = TripAdvisor_fft_df['TripAdvisor_final_fft'].apply(lambda x: np.abs(x))

TripAdvisor_fft_df['TripAdvisor_fft_angle'] = TripAdvisor_fft_df['TripAdvisor_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

TripAdvisor_fft_list = np.asarray(TripAdvisor_fft_df['TripAdvisor_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    TripAdvisor_fft_list_m10= np.copy(TripAdvisor_fft_list); TripAdvisor_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(TripAdvisor_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(TripAdvisor_FT['TripAdvisor_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: TripAdvisor (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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​

#TwentyFirst_Century_Fox_A_FFT

TwentyFirst_Century_Fox_A_FT = SP500_TechIndicator[['Date', 'TwentyFirst_Century_Fox_A_Close']]

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TwentyFirst_Century_Fox_A_Close_fft = np.fft.fft(np.asarray(TwentyFirst_Century_Fox_A_FT['TwentyFirst_Century_Fox_A_Close'].tolist()))

TwentyFirst_Century_Fox_A_fft_df = pd.DataFrame({'TwentyFirst_Century_Fox_A_final_fft':TwentyFirst_Century_Fox_A_Close_fft})

TwentyFirst_Century_Fox_A_fft_df['TwentyFirst_Century_Fox_A_fft_absolute'] = TwentyFirst_Century_Fox_A_fft_df['TwentyFirst_Century_Fox_A_final_fft'].apply(lambda x: np.abs(x))

TwentyFirst_Century_Fox_A_fft_df['TwentyFirst_Century_Fox_A_fft_angle'] = TwentyFirst_Century_Fox_A_fft_df['TwentyFirst_Century_Fox_A_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

TwentyFirst_Century_Fox_A_fft_list = np.asarray(TwentyFirst_Century_Fox_A_fft_df['TwentyFirst_Century_Fox_A_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    TwentyFirst_Century_Fox_A_fft_list_m10= np.copy(TwentyFirst_Century_Fox_A_fft_list); TwentyFirst_Century_Fox_A_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(TwentyFirst_Century_Fox_A_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(TwentyFirst_Century_Fox_A_FT['TwentyFirst_Century_Fox_A_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: TwentyFirst_Century_Fox_A (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

​

​

#TwentyFirst_Century_Fox_B_FFT

TwentyFirst_Century_Fox_B_FT = SP500_TechIndicator[['Date', 'TwentyFirst_Century_Fox_B_Close']]

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TwentyFirst_Century_Fox_B_Close_fft = np.fft.fft(np.asarray(TwentyFirst_Century_Fox_B_FT['TwentyFirst_Century_Fox_B_Close'].tolist()))

TwentyFirst_Century_Fox_B_fft_df = pd.DataFrame({'TwentyFirst_Century_Fox_B_final_fft':TwentyFirst_Century_Fox_B_Close_fft})

TwentyFirst_Century_Fox_B_fft_df['TwentyFirst_Century_Fox_B_fft_absolute'] = TwentyFirst_Century_Fox_B_fft_df['TwentyFirst_Century_Fox_B_final_fft'].apply(lambda x: np.abs(x))

TwentyFirst_Century_Fox_B_fft_df['TwentyFirst_Century_Fox_B_fft_angle'] = TwentyFirst_Century_Fox_B_fft_df['TwentyFirst_Century_Fox_B_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

TwentyFirst_Century_Fox_B_fft_list = np.asarray(TwentyFirst_Century_Fox_B_fft_df['TwentyFirst_Century_Fox_B_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    TwentyFirst_Century_Fox_B_fft_list_m10= np.copy(TwentyFirst_Century_Fox_B_fft_list); TwentyFirst_Century_Fox_B_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(TwentyFirst_Century_Fox_B_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(TwentyFirst_Century_Fox_B_FT['TwentyFirst_Century_Fox_B_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: TwentyFirst_Century_Fox_B (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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#Verizon_Communications_FFT

Verizon_Communications_FT = SP500_TechIndicator[['Date', 'Verizon_Communications_Close']]

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Verizon_Communications_Close_fft = np.fft.fft(np.asarray(Verizon_Communications_FT['Verizon_Communications_Close'].tolist()))

Verizon_Communications_fft_df = pd.DataFrame({'Verizon_Communications_final_fft':Verizon_Communications_Close_fft})

Verizon_Communications_fft_df['Verizon_Communications_fft_absolute'] = Verizon_Communications_fft_df['Verizon_Communications_final_fft'].apply(lambda x: np.abs(x))

Verizon_Communications_fft_df['Verizon_Communications_fft_angle'] = Verizon_Communications_fft_df['Verizon_Communications_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

Verizon_Communications_fft_list = np.asarray(Verizon_Communications_fft_df['Verizon_Communications_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Verizon_Communications_fft_list_m10= np.copy(Verizon_Communications_fft_list); Verizon_Communications_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Verizon_Communications_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Verizon_Communications_FT['Verizon_Communications_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Verizon_Communications (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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#Viacom_FFT

Viacom_FT = SP500_TechIndicator[['Date', 'Viacom_Close']]

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Viacom_Close_fft = np.fft.fft(np.asarray(Viacom_FT['Viacom_Close'].tolist()))

Viacom_fft_df = pd.DataFrame({'Viacom_final_fft':Viacom_Close_fft})

Viacom_fft_df['Viacom_fft_absolute'] = Viacom_fft_df['Viacom_final_fft'].apply(lambda x: np.abs(x))

Viacom_fft_df['Viacom_fft_angle'] = Viacom_fft_df['Viacom_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

Viacom_fft_list = np.asarray(Viacom_fft_df['Viacom_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    Viacom_fft_list_m10= np.copy(Viacom_fft_list); Viacom_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(Viacom_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(Viacom_FT['Viacom_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: Viacom (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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#The_Walt_Disney_FFT

The_Walt_Disney_FT = SP500_TechIndicator[['Date', 'The_Walt_Disney_Close']]

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The_Walt_Disney_Close_fft = np.fft.fft(np.asarray(The_Walt_Disney_FT['The_Walt_Disney_Close'].tolist()))

The_Walt_Disney_fft_df = pd.DataFrame({'The_Walt_Disney_final_fft':The_Walt_Disney_Close_fft})

The_Walt_Disney_fft_df['The_Walt_Disney_fft_absolute'] = The_Walt_Disney_fft_df['The_Walt_Disney_final_fft'].apply(lambda x: np.abs(x))

The_Walt_Disney_fft_df['The_Walt_Disney_fft_angle'] = The_Walt_Disney_fft_df['The_Walt_Disney_final_fft'].apply(lambda x: np.angle(x))

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plt.figure(figsize=(14, 7), dpi=100)

The_Walt_Disney_fft_list = np.asarray(The_Walt_Disney_fft_df['The_Walt_Disney_final_fft'].tolist())

for num_ in [3, 6, 9, 100]:

    The_Walt_Disney_fft_list_m10= np.copy(The_Walt_Disney_fft_list); The_Walt_Disney_fft_list_m10[num_:-num_]=0

    plt.plot(np.fft.ifft(The_Walt_Disney_fft_list_m10), label='Fourier transform with {} components'.format(num_))

plt.plot(The_Walt_Disney_FT['The_Walt_Disney_Close'],  label='Real')

plt.xlabel('Days')

plt.ylabel('USD')

plt.title('Figure 3: The_Walt_Disney (close) stock prices & Fourier transforms')

plt.legend()

plt.show()

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​

Communication_Services_FFT = pd.concat((Activision_Blizzard_fft_df,ATT_fft_df,CBS_fft_df,CenturyLink_fft_df,Comcast_fft_df, Discovery_Class_A_fft_df, Discovery_Class_C_fft_df,Dish_fft_df,Electronic_Arts_fft_df,Facebook_fft_df, Interpublic_Group_fft_df, Netflix_fft_df, News_Corp_Class_A_fft_df, News_Corp_Class_B_fft_df, Omnicom_Group_fft_df, Take_Two_Interactive_fft_df, Twitter_fft_df, TripAdvisor_fft_df, TwentyFirst_Century_Fox_A_fft_df, TwentyFirst_Century_Fox_B_fft_df, Verizon_Communications_fft_df, Viacom_fft_df, The_Walt_Disney_fft_df), axis=1, join='inner')

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Communication_Services_FFT

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